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Siegler, Robert; Carpenter, Thomas; Fennell, Francis; Geary, David; Lewis, James; Okamoto, Yukari; Thompson, Laurie; Wray, Jonathan – What Works Clearinghouse, 2010
This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…
Descriptors: Mathematics, Problem Solving, Young Children, Elementary Education
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Jacobs, Victoria R.; Franke, Megan Loef; Carpenter, Thomas P.; Levi, Linda; Battey, Dan – Journal for Research in Mathematics Education, 2007
A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…
Descriptors: Faculty Development, Algebra, Mathematical Logic, Thinking Skills
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Steinberg, Ruth M.; Empson, Susan B.; Carpenter, Thomas P. – Journal of Mathematics Teacher Education, 2004
In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's…
Descriptors: Inquiry, Educational Change, Case Studies, Mathematics Teachers
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda – 2003
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
Descriptors: Algebra, Arithmetic, Elementary Education, Mathematics Activities
Carpenter, Thomas P.; Levi, Linda – 2000
This report describes a research project that investigated how to design instruction to help children take the step to generalizing and formalizing their knowledge into powerful abstract systems for representing and operating mathematical ideas. The studies build on existing research on cognitively guided instruction (CGI). The goal of this paper…
Descriptors: Algebra, Elementary Education, Mathematics Curriculum, Mathematics Instruction
Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed. – Lawrence Erlbaum Associates (Bks), 2005
The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…
Descriptors: Teaching Methods, Science Instruction, Mathematics Instruction, Mathematics Education
Carpenter, Thomas P.; Levi, Linda; Farnsworth, Valerie – In Brief, 2000
"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…
Descriptors: Abstract Reasoning, Algebra, Arithmetic, Educational Change
Fennema, Elizabeth; Sowder, Judith; Carpenter, Thomas P. – 1999
This chapter builds on the idea that classrooms that promote understanding can and do exist. Elaborating upon this idea the question is raised, "In what ways can many more classrooms be developed so that all students have the opportunity to learn with understanding?" The construction of classrooms that promote understanding is dependent upon…
Descriptors: Classroom Environment, Educational Research, Elementary Secondary Education, Instructional Effectiveness
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Falkner, Karen P.; Levi, Linda; Carpenter, Thomas P. – Teaching Children Mathematics, 1999
Discusses the concept of equality, which is a crucial idea for developing algebraic reasoning in young children. Explores young children's understanding and misconceptions about the "equals" sign, and relates the experiences one teacher had helping children better understand the sign. (ASK)
Descriptors: Elementary Education, Elementary School Mathematics, Mathematics Instruction, Misconceptions
Carpenter, Thomas P.; Fennema, Elizabeth; Franke, Megan Loef; Levi, Linda; Empson, Susan B. – 2000
This paper describes a research-based teacher professional development program for elementary school mathematics and includes an overview of cognitively guided instruction (CGI). Also described are the CGI professional development program and the research base for CGI with regard to children's thinking; teachers' knowledge and beliefs about…
Descriptors: Academic Achievement, Elementary Education, Faculty Development, Mathematics Education
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Carpenter, Thomas P.; And Others – Elementary School Journal, 1996
Suggests that children enter school with a great deal of informal intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. Describes a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or…
Descriptors: Addition, Cognitive Development, Cognitive Processes, Division
Carpenter, Thomas P.; Fennema, Elizabeth; Franke, Megan Loef; Levi, Linda; Empson, Susan B. – 1999
This book, with accompanying CD-ROMs, was written to help readers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. Detailed…
Descriptors: Cognitive Processes, Concept Formation, Educational Strategies, Elementary Education
Carpenter, Thomas; And Others – 1978
This monograph is a comprehensive presentation and discussion of the 1972-73 National Assessment mathematics data. It is a report from the National Council of Teachers of Mathematics Project for Interpretive Reports on National Assessment. The report examines data from four age groups (nine, thirteen, seventeen, and adult) and evaluates…
Descriptors: Adult Education, Data Analysis, Educational Assessment, Educational Research
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Carpenter, Thomas P. – 1972
Reported is a study of the development of conservation and measurement concepts, with reference to certain task factors which may affect performance. A group of 129 first and second graders were given a test of conservation and measurement consisting of five problem types crossed with three transformation types. The problems all involved moving…
Descriptors: Conservation (Concept), Elementary School Mathematics, Grade 1, Grade 2
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Carpenter, Thomas P. – Education and Urban Society, 1985
Children's solutions to simple word problems requiring addition or subtraction skills develop through four stages: (1) modeling with objects; (2) utilization of both modeling and counting strategies; (3) reliance on counting strategies; and (4) reliance on number facts. The current primary mathematics curriculum fails to capitilize on rich…
Descriptors: Arithmetic, Informal Education, Learning Processes, Mathematics Curriculum
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